First Law of Thermodynamics · Thermodynamics · GATE ME

Consider 1 kg of an ideal gas at 1 bar and 300 K contained in a rigid and perfectly insulated container. The specific heat of the gas at constant volume c_v is equal to 750 J-kg^-1K^-1. A stirrer performs 225 kJ of work on the gas. Assume that the container does not participate in the thermodynamic interaction. The final pressure of the gas will be ______ bar (in integer). 

Water (density $$ = 1000$$ $$kg/{m^3}$$) at ambient temperature flows through a horizontal pipe of uniform cross section at the rate of $$1$$ $$kg/s.$$ If the pressure drop across the pipe is $$100$$ $$kPa,$$ the minimum power required to pump the water across the pipe, in watts, is

A gas contained in a cylinder is compressed, the work required for compression being $$5000$$ $$kJ.$$ During the process, heat interaction of $$200$$ $$kJ$$ causes the surroundings to the heated. The change in internal energy of the gas during the process is

A $$2$$ $$kW,$$ $$40$$ liter water heater is switched on for $$20$$ minutes. The heat capacity $${C_p}$$ for water is $$4.2$$ $$kJ/kg$$ $$K.$$ Assuming all the electrical energy has gone into heating the water, increase of the water temperature in degree centigrade is

A steam turbine receives steam steadily at $$10$$ $$bar$$ with an enthalpy of $$3000$$ $$kJ/kg$$ and discharges at $$1$$ bar with an enthalpy of $$2700$$ $$kJ/kg.$$ The work output is $$250$$ $$kJ/kg.$$ The changes in kinetic and potential energies are negligible. The heat transfer from the turbine casing to the surroundings is equal to

A steel ball of mass $$1$$ $$kg$$ and specific heat $$0.4$$ $$kJ/kg$$ is at temperature of $${60^ \circ }C.$$ It is dropped into $$1$$ $$kg$$ water at $${20^ \circ }C.$$ The final steady state temperature of water is

The first law of thermodynamics takes the form $$W = - \Delta \,H$$ when applied to :

Which one of the following statements is FALSE?

Consider a fully adiabatic piston-cylinder arrangement as shown in the figure. The piston is massless and cross-sectional area of the cylinder is 𝐴. The fluid inside the cylinder is air (considered as a perfect gas), with γ being the ratio of the specific heat at constant pressure to the specific heat at constant volume for air. The piston is initially located at a position 𝐿1. The initial pressure of the air inside the cylinder is 𝑃₁ ≫ 𝑃₀, where 𝑃₀ is the atmospheric pressure. The stop S₁ is instantaneously removed and the piston moves to the position 𝐿₂, where the
equilibrium pressure of air inside the cylinder is 𝑃₂ ≫ 𝑃₀.

What is the work done by the piston on the atmosphere during this process?

A rigid tank of volume of 8 m³ is being filled up with air from a pipeline connected through a valve. Initially the valve is closed and the tank is assumed to be completely evacuated. The air pressure and temperature inside the pipeline are maintained at 600 kPa and 306 K, respectively. The filling of the tank begins by opening the valve and the process ends when the tank pressure is equal to the pipeline pressure. During the filling process, heat loss to the surrounding is 1000 kJ. The specific heats of air at constant pressure and at constant volume are 1.005 kJ/kg.K and 0.718 kJ/kg.K, respectively. Neglect changes in kinetic energy and potential energy.

The final temperature of the tank after the completion of the filling process is ________ K (round off to the nearest integer). 

An engine running on an air standard Otto cycle has a displacement volume 250 cm³ and a clearance volume 35.7 cm³. The pressure and temperature at the beginning of the compression process are 100 kPa and 300 K, respectively. Heat transfer during constant-volume heat addition process is 800 kJ/kg. The specific heat at constant volume is 0.718 kJ/kg.K and the ratio of specific heats at constant pressure and constant volume is 1.4. Assume the specific heats to remain constant during the cycle. The maximum pressure in the cycle is ______ kPa (round off to the nearest integer).

One $$kg$$ of an ideal gas (gas constant, $$R = 400$$ $$J/kg.K;$$ specific heat at constant volume, $${c_v} = 1000\,J/kg.K$$ at $$1$$ bar, and $$300$$ $$K$$ is contained in a sealed rigid cylinder. During an adiabatic process, $$100$$ $$kJ$$ of work is done on the system by a stirrer. The increase in entropy of the system is _________ $$J/K.$$

A calorically perfect gas (specific heat at constant pressure $$1000$$$$J/kg.K$$) enters and leaves a gas turbine with the same velocity. The temperatures of the gas at turbine entry and exit are $$1100K$$ and $$400K.$$ respectively. The power produced is $$4.6MW$$ and heat escapes at the rate of $$300kJ/s$$ through the turbine casing. The mass flow rate of the gas (in $$kg/s$$) through the turbine is.

A piston-cylinder device initially contains $$0.4\,{m^3}$$ of air (to be treated as an ideal gas) at $$100$$ $$kPa$$ and $${80^ \circ }C.$$ The air is now isothermally compressed to 0.1 m3 . The work done during this process is ________ $$kJ.$$

(Take the sign convention such that work done on the system is negative)

Steam at an initial enthalpy of $$100$$ $$kJ/kg$$ and inlet velocity of $$100$$ $$m/s,$$ enters an insulated horizontal nozzle. It leaves the nozzle at $$200$$ $$m/s.$$ The exit enthalpy (in $$kJ/kg$$) is ___________

Work is done on an adiabatic system due to which its velocity changes from $$10$$ $$m/s$$ to $$20$$ $$m/s,$$ elevation increases by $$20$$ $$m$$ and temperature increases by $$1$$ $$K$$. The mass of the system is $$10$$ $$kg,$$ $${{C_v} = 100J\left( {kg.K} \right)}$$ and gravitational acceleration is $$10\,\,m/{s^2}.$$ If there is no change in any other component of the energy of the system, the magnitude of total work done (in $$kJ$$) on the system is _______________.

A well insulated rigid container of volume $$1{m^3}$$ contains $$1.0$$ $$kg$$ of an ideal gas $$\left[ {{C_p} =1000\,\,\,J/\left( {kg.K} \right)} \right.$$ and $$\left. {{C_v} = 800J/\left( {kg.K} \right)} \right]$$ at a pressure of $${10^5}\,\,Pa.$$ A stirrer is rotated at constant $$rpm$$ in the container for $$1000$$ rotations and the applied torque is $$100$$ $$N$$-$$m.$$ The final temperature of the gas (in $$K$$) is _______________.

Specific enthalpy and velocity of steam at inlet and exit of a steam turbine, running under steady state, are as given below:

The rate of heat loss from the turbine per $$kg$$ of steam flow rate is $$5$$ $$kW.$$ Neglecting changes in potential energy of steam, the power developed in $$kW$$ by the steam turbine per $$kg$$ of steam flow rate, is

Air enters an adiabatic nozzle at $$300$$ $$kPa,$$ $$500$$ $$K$$ with a velocity of $$10$$ $$m/s.$$ It leaves the nozzle at $$100$$ $$kPa$$ with a velocity of $$180$$ $$m/s.$$ The inlet area is $$80$$ $$c{m^2}.$$ The specific heat of air $${C_p}$$ is $$1008$$ $$J/kg.K.$$

The exit temperature of the air is

Air enters an adiabatic nozzle at $$300$$ $$kPa,$$ $$500$$ $$K$$ with a velocity of $$10$$ $$m/s.$$ It leaves the nozzle at $$100$$ $$kPa$$ with a velocity of $$180$$ $$m/s.$$ The inlet area is $$80$$ $$c{m^2}.$$ The specific heat of air $${C_p}$$ is $$1008$$ $$J/kg.K.$$

The exit area of the nozzle in $$c{m^2}$$ is

Steam enters an adiabatic turbine operating at steady state with an enthalpy of $$3251.0kJ/kg$$ and leaves as a saturated mixture at $$15$$ $$kPa$$ with quality (dryness fraction ) $$0.9.$$ The enthalpies of the saturated liquid and vapour at $$15$$ $$kPa$$ are $${h_f} = 225.94kJ/kg$$ and $${h_g} = 2598.3kJ/kg$$ respectively. The mass flow rate of steam is $$10kg/s.$$ Kinetic and potential energy changes are negligible. The power output of the turbine in $$MW$$ is

The temperature and pressure of air in a large reservoir are $$400$$ $$K$$ and $$3$$ bar respectively. A converging diverging nozzle of exit area $$0.005{m^2}$$ is fitted to the wall of the reservoir as shown in the figure. The static pressure of air at the exit section for isentropic flow through the nozzle is $$50$$ $$kPa.$$ The characteristic gas constant and the ratio of specific heats of air are $$0.287$$ $$kJ/kgK$$ and $$1.4$$ respectively.

The mass flow rate of air through the nozzle in $$kg/s$$ is

The temperature and pressure of air in a large reservoir are $$400$$ $$K$$ and $$3$$ bar respectively. A converging diverging nozzle of exit area $$0.005{m^2}$$ is fitted to the wall of the reservoir as shown in the figure. The static pressure of air at the exit section for isentropic flow through the nozzle is $$50$$ $$kPa.$$ The characteristic gas constant and the ratio of specific heats of air are $$0.287$$ $$kJ/kgK$$ and $$1.4$$ respectively.

The density of air in $$kg/{m^3}$$ at the nozzle exit is

A balloon containing an ideal gas is initially kept in an evacuated and insulated room. The balloon ruptures and the gas fills up the entire room. Which one of the following statements is TRUE at the end of above process?

A rigid, insulated tank is initially evacuated. The tank is connected with a supply line through which air ( assumed to be ideal gas with constant specific heats) passes at $$1$$ $$MPa,$$ $${350^ \circ }C.$$ A valve connected with the supply line is opened and the tank is charged with air until the final pressure inside the tank reaches $$1$$ $$MPa.$$ The final temperature inside the tank.

What is the speed of sound in Neon gas at a temperature of $$500$$ $$K$$ (Gas constant of Neon is $$0.4210$$ $$kJ/kg$$-$$K$$)?

A small steam whistle (perfectly insulated and doing no shaft work) causes a drop of $$0.8$$ $$kJ/kg$$ in the enthalpy of steam from entry to exit. If the kinetic energy of the steam at entry is negligible, the velocity of the steam at exit is

When an ideal gas with constant specific heats is throttled adiabatically, with negligible changes in kinetic and potential energies

A rigid insulated cylinder has two compartments separated by a thin membrane. While one compartment contains one kmol nitrogen at a certain pressure and temperature, the other contains one kmol carbon dioxide at the same pressure and temperature. The membrane is ruptured and the two gases are allowed to mix.

Assume that the gases behave as ideal gases. Calculate the increase in entropy of the contents of the cylinder. Universal gas constant equal to $$8314.3$$ $$J/kmol$$ $$K.$$

A certain mass of a pure substance undergoes an irreversible process from state $$1$$ to state $$2,$$ the path of the process being a straight line on the $$T$$-$$s$$ diagram. Calculate heat transfer & work done. Some of the properties at the initial and final states are:
$${T_1} = 330\,K,\,\,{T_2} = 440\,K;\,\,{U_1} = 170\,kJ,\,\,$$
$$\,{U_2} = 190\,kJ;\,\,{H_1} = 220{\,_{}}kJ,\,\,{H_2} = 247\,kJ,$$
and $${S_1} = 0.23\,kJ/K$$ and $${S_2} = 0.3\,kJ/K$$ where $$T, U, H$$ and $$S$$ represent temperature, internal energy, enthalpy and entropy respectively.

Air enters a frictionless adiabatic converging nozzle at $$10$$ bar, $$500$$ $$K$$ with negligible velocity. The nozzle dis-charges to a region at $$2$$ bar. If the exit area of the nozzle is $$2.5\,c{m^2}$$ find the flow rate of air through the nozzle. Assume for air, $${C_p} = 1005\,J/kg\,K$$ and $${C_v} = 718\,J/kg\,K.$$